Twisting Lightlike Solutions of the Kerr-Schild Class

TL;DR

This paper introduces a method to construct boosted Kerr geometries with twist, revealing that twist helps eliminate singularities and smooth shock waves in ultrarelativistic limits, differing from known pp-wave solutions.

Contribution

It presents a novel approach using complex representation and Kerr theorem to generate twisting ultrarelativistic Kerr solutions with non-zero angular momentum.

Findings

Twisting solutions retain angular momentum in ultrarelativistic limit.

Twist prevents singularities and smooths shock waves.

Method applies to two different physical scenarios.

Abstract

Using a complex representation of the Debney-Kerr-Schild (DKS) solutions and the Kerr theorem we give a method to construct boosted Kerr geometries. In the ultrarelativistic case this method yelds twisting solutions having, contrary to the known pp-wave limiting solutions, a non-zero value of the total angular momentum. The solutions show that twist plays a crucial role in removing singularity and smoothing shock wave in the ultrarelativistic limit. Two different physical situations are discussed.